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The problem states:

- There are 50 integrated circuits.
- The probability that any integrated circuit is defective is \( P(\text{defective}) = 0.03 \).
- The integrated circuits are independent of one another.
- The product operates only if **none** of the circuits are defective.

To find the probability that the product operates, we need to calculate the probability that **none** of the circuits are defective. This is equivalent to calculating the probability that each of the 50 circuits works.

1. The probability that a circuit is **not defective** is:
   \[
   P(\text{not defective}) = 1 - 0.03 = 0.97
   \]

2. The product will work if all 50 circuits are not defective. Since the circuits are independent, the probability that all 50 circuits are not defective is the product of the individual probabilities:
   \[
   P(\text{operates}) = 0.97^{50}
   \]

Let me calculate that value.The probability that the product operates (i.e., none of the 50 integrated circuits are defective) is approximately \( 0.2181 \).

Would you like further clarification or details?

Here are five related questions for further exploration:
1. How would the probability change if the number of circuits increased to 100?
2. What if the probability of a defective circuit were 0.05 instead of 0.03?
3. How does this problem relate to the binomial distribution?
4. Can we generalize this method for products with varying numbers of circuits?
5. How would the solution change if the circuits were not independent?

**Tip:** When dealing with probabilities of independent events, the overall probability of all events occurring is the product of their individual probabilities.

An electronic product contains 50 integrated circuits. The probability that any integrated circuit is defective is 0.03, and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. What is the probability that the product operates? Round your answer to four decimal places.

Calculate the probability that an electronic product with 50 independent integrated circuits operates when the probability of a defective circuit is 0.03. Learn about independent event probability and the key formula P(operates) = P(not defective)^50.

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